Focus,
you are correct. The crack is no proove that it was your fault. There is indeed the possibility, that the screen was slightly cracked already, when you got it and with a minimum of pressure it broke.

I love these legal discussions by "laypeople".
Beyound the leagal responsibilities of the seller/producer there is something like goodwill(german: Kulanz).
Then this could be applied in not so clear cases.
Anyway: what is the use of a device that breaks so easily?